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Is the role of the boxed condition $z'(t)neq 0$ to avoid going back?
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The role of the boxed condition $z'(t)neq 0$ is to avoid going back, isn't it?
complex-analysis curves complex-integration plane-curves
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The role of the boxed condition $z'(t)neq 0$ is to avoid going back, isn't it?
complex-analysis curves complex-integration plane-curves
asked yesterday
Born to be proud
770510
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The role of the boxed condition $z'(t)neq 0$ is to avoid going back, isn't it?
complex-analysis curves complex-integration plane-curves
asked yesterday
Born to be proud
770510
The role of the boxed condition $z'(t)neq 0$ is to avoid going back, isn't it?
complex-analysis curves complex-integration plane-curves
complex-analysis curves complex-integration plane-curves
asked yesterday
Born to be proud
770510
asked yesterday
Born to be proud
770510
asked yesterday
Born to be proud
770510
asked yesterday
Born to be proud
770510
asked yesterday
Born to be proud
770510
770510
add a comment |
add a comment |
1 Answer
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No. It is so that the velocity is never $0$, which implies that we can parametrize the curve by the arc length. It also implies that $zbigl([a,b]bigr)$ has no “corners”, which corresponds to the idea of a smooth curve.
answered yesterday
José Carlos Santos
139k18111203
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
No. It is so that the velocity is never $0$, which implies that we can parametrize the curve by the arc length. It also implies that $zbigl([a,b]bigr)$ has no “corners”, which corresponds to the idea of a smooth curve.
answered yesterday
José Carlos Santos
139k18111203
add a comment |
up vote
0
down vote
No. It is so that the velocity is never $0$, which implies that we can parametrize the curve by the arc length. It also implies that $zbigl([a,b]bigr)$ has no “corners”, which corresponds to the idea of a smooth curve.
answered yesterday
José Carlos Santos
139k18111203
add a comment |
up vote
0
down vote
up vote
0
down vote
No. It is so that the velocity is never $0$, which implies that we can parametrize the curve by the arc length. It also implies that $zbigl([a,b]bigr)$ has no “corners”, which corresponds to the idea of a smooth curve.
answered yesterday
José Carlos Santos
139k18111203
No. It is so that the velocity is never $0$, which implies that we can parametrize the curve by the arc length. It also implies that $zbigl([a,b]bigr)$ has no “corners”, which corresponds to the idea of a smooth curve.
answered yesterday
José Carlos Santos
139k18111203
answered yesterday
José Carlos Santos
139k18111203
answered yesterday
José Carlos Santos
139k18111203
answered yesterday
José Carlos Santos
139k18111203
139k18111203
add a comment |
add a comment |
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